Because your EFC is not affordable, you are going to have to apply to schools that give significant merit aid….The plus is that you have great in-state options, assuming the publics are all affordable for you.
Some of the publics where you are OOS will have to come off your list….for example, UIUC is not going to get to your price range. OSU and Clemson probably won’t either, but they do give more merit than UIUC, so makes sense to try.
I can’t find more recent data, But VT’s average engineering SAT math score was 707 for class of 2023, so I recommend you apply TO there. What does your HS GC say about TO or not at VT? About Virginia Tech Engineering | Engineering | Virginia Tech